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A095778 Values of n for which A095777(n) is 9 (those terms which are expressible in decimal digits for bases 2 through 10, but not for base 11).

%I A095778 #19 Dec 06 2024 07:34:47
%S A095778 10,21,32,43,54,65,76,87,98,109,110,111,112,113,114,115,116,117,118,
%T A095778 119,120,131,142,153,164,175,186,197,208,219,230,231,232,233,234,235,
%U A095778 236,237,238,239,240,241,252,263,274,285,296,307,318,329,340,351,352,353
%N A095778 Values of n for which A095777(n) is 9 (those terms which are expressible in decimal digits for bases 2 through 10, but not for base 11).
%C A095778 Numbers with at least one digit A (=10) in their representation in base 11. Complementary sequence to A171397. - _François Marques_, Oct 11 2020
%H A095778 François Marques, <a href="/A095778/b095778.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale)
%e A095778 a(5)=54 because 54 when expressed in successive bases starting at 2 will produce its first non-decimal digit at base 11. Like so: 110110, 2000, 312, 204, 130, 105, 66, 60, 54. In base 11, 54 is 4A.
%p A095778 S := []; for n from 1 to 1000 do; if 1>0 then; ct := 0; ok := true; b := 2; if (n>9) then; while ok=true do; L := convert(n, base, b); for e in L while ok=true do; if (e > 9) then ok:=false; fi; od; if ok=true then; ct := ct + 1; b := b + 1; fi; od; fi; if ct=9 then S := [op(S), n]; fi; fi; od; S;
%p A095778 # or
%p A095778 seq(`if`(numboccur(10, convert(n, base, 11))>0, n, NULL), n=0..1000); # _François Marques_, Oct 11 2020
%t A095778 Select[Range[400],Max[IntegerDigits[#,11]]>9&] (* _Harvey P. Dale_, Sep 30 2018 *)
%o A095778 (PARI) isok(m) = #select(x->(x==10), digits(m, 11)) >= 1; \\ _François Marques_, Oct 11 2020
%o A095778 (Python)
%o A095778 from gmpy2 import digits
%o A095778 def A095778(n):
%o A095778     def f(x):
%o A095778         l = (s:=digits(x,11)).find('a')
%o A095778         if l >= 0: s = s[:l]+'9'*(len(s)-l)
%o A095778         return n+int(s)
%o A095778     m, k = n, f(n)
%o A095778     while m != k: m, k = k, f(k)
%o A095778     return m # _Chai Wah Wu_, Dec 04 2024
%Y A095778 Cf. A095777.
%Y A095778 Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), this sequence (b=11).
%Y A095778 Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).
%K A095778 base,nonn
%O A095778 1,1
%A A095778 Chuck Seggelin (seqfan(AT)plastereddragon.com), Jun 05 2004